Two circles x2+y2+2g1x+2f1y+c1=0 and x2+y2+2g2x+2f2y+c2=0 are said to be orthogonal. Then 2g1g2+2f1f2=c1+c2
True
Given circles x2+y2+2g1x+2f1y+c=0 .......(1)
x2+y2+2g2x+2f2y+c=0 ............(2)
Let C1& C2 be the centers and r1& r2 radii of circle (1) and (2) respectively. P& Q is the point of
intersection of two circles
C1(−g1−f1)
C2(−g2−f2)
r1=√g21+f21−c1,r2=√g22+f22−c2
C1P=r1
C2P=r2
Right angle triangle C1PC2
(c1c2)2=r21+r22
(g1−g2)2+(f1−f2)2=g21+f21−c1+g22+f22−c2
2g1g2+2f1f2=c1+c2
So, give statemebt is correct.